Divide and conquer: An incremental sparsity promoting compressive sampling approach for polynomial chaos expansions

Negin Alemazkoor, Hadi Meidani

Research output: Contribution to journalArticle

Abstract

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional expansions for a sparser recovery, and shows success when removal of uninfluential parameters that results in a lower coherence for measurement matrix, allows for a higher order and/or sparser expansion to be recovered. The incremental algorithm effectively searches for the sparsest PC approximation, and not only can it decrease the prediction error, but it can also reduce the dimensionality of PCE model. Four numerical examples are provided to demonstrate the validity of the proposed approach. The results from these examples show that the incremental algorithm substantially outperforms conventional compressive sampling approaches for PCE, in terms of both solution sparsity and prediction error.

Original languageEnglish (US)
Pages (from-to)937-956
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Volume318
DOIs
StatePublished - May 1 2017

Keywords

  • Compressive sampling
  • Legendre polynomials
  • Polynomial chaos expansion
  • Sparse approximation
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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